Tyendinaga Data

Notes:

• data exported from 'Student' computer
• using data with filename Tyendinaga1_001.asc as main data source to make plots with
• Tyendinaga1_001.asc data was recorded on Oct. 26, 2025 from 18:07:12 to 18:27:12

Version Notes:
pandas: 2.2.2
numpy: 1.26.4
scipy: 1.16.3

DataFrame --> File Name Legend:

• df --> Tyendinaga_001.asc
• df2 --> Tyendinaga2_001.asc
• df3 --> Tyendinaga3_001.asc
• df4 --> Tyendinaga4_001.asc
• df5 --> Tyendinaga5_001.asc

Check for null values:

• will show "False" if no null values

df:  False
df2: False
df3: False
df4: False
df5: False

Columns of Interest:

• NS: North-South component of motion
• EW: East-West component of motion
• Z: Vertical (Z-axis) component of motion

Other Notes:

• Sampling rate for all files: 1024 Hz
• See below for preview of the data:

dataframe: df
      NS     EW      Z  nsL  ewL    zL     aY     aX    aZ  time (s)
0  273.0  269.0  862.0  8.0  8.0  26.0  125.0  244.0  10.0  0.000000
1  276.0  274.0  864.0  8.0  8.0  27.0  127.0  247.0   9.0  0.000977
2  273.0  276.0  864.0  8.0  8.0  27.0  127.0  243.0  12.0  0.001953
3  271.0  274.0  860.0  8.0  8.0  26.0  127.0  246.0   3.0  0.002930
4  273.0  270.0  854.0  8.0  8.0  26.0  128.0  247.0   7.0  0.003906

dataframe: df2
      NS     EW      Z  nsL   ewL    zL     aY     aX    aZ  time (s)
0  271.0  270.0  852.0  8.0   8.0  26.0  224.0  169.0  23.0  0.000000
1  269.0  286.0  868.0  8.0   8.0  27.0  224.0  172.0  17.0  0.000977
2  268.0  307.0  869.0  8.0   9.0  27.0  224.0  173.0  18.0  0.001953
3  266.0  320.0  861.0  8.0  10.0  26.0  224.0  173.0  21.0  0.002930
4  263.0  323.0  856.0  8.0  10.0  26.0  223.0  172.0  18.0  0.003906

dataframe: df3
      NS     EW      Z  nsL  ewL    zL     aY     aX    aZ  time (s)
0  264.0  273.0  845.0  8.0  8.0  26.0  192.0  210.0  19.0  0.000000
1  258.0  270.0  842.0  8.0  8.0  26.0  192.0  206.0  21.0  0.000977
2  259.0  269.0  838.0  8.0  8.0  26.0  192.0  198.0  18.0  0.001953
3  256.0  266.0  834.0  8.0  8.0  26.0  192.0  196.0  16.0  0.002930
4  253.0  260.0  833.0  7.0  8.0  26.0  192.0  204.0  19.0  0.003906

dataframe: df4
      NS     EW      Z  nsL  ewL    zL     aY     aX    aZ  time (s)
0  245.0  256.0  847.0  7.0  8.0  26.0  118.0  172.0  -8.0  0.000000
1  243.0  256.0  840.0  7.0  8.0  26.0  118.0  171.0  -8.0  0.000977
2  243.0  260.0  840.0  7.0  8.0  26.0  115.0  171.0 -14.0  0.001953
3  244.0  264.0  840.0  7.0  8.0  26.0  115.0  168.0 -13.0  0.002930
4  248.0  265.0  843.0  7.0  8.0  26.0  114.0  169.0 -15.0  0.003906

dataframe: df5
      NS     EW      Z  nsL  ewL    zL     aY     aX   aZ  time (s)
0  283.0  267.0  874.0  8.0  8.0  27.0  127.0  128.0  8.0  0.000000
1  281.0  269.0  876.0  8.0  8.0  27.0  127.0  128.0  3.0  0.000977
2  282.0  272.0  870.0  8.0  8.0  27.0  126.0  128.0  6.0  0.001953
3  280.0  278.0  859.0  8.0  8.0  26.0  126.0  128.0  7.0  0.002930
4  275.0  281.0  851.0  8.0  8.0  26.0  126.0  128.0  6.0  0.003906

---

Plotting the Time Series

Notes:

• Plot the NS, EW, and Z data separately

dataframe: df

dataframe: df2

dataframe: df3

dataframe: df4

dataframe: df5

---

Normalizing, Detrending and Shifting Data

Notes:

• data range of time series was normalized using MinMaxScaler from sklearn
• data was linearly detrended using signal.detrend from scipy
• the mean of the data was shifted to zero

dataframe: df
NS Min-Max normalized range: [0.000, 1.000]
EW Min-Max normalized range: [0.000, 1.000]
Z Min-Max normalized range: [0.000, 1.000]
New range for NS: [-0.515, 0.485]
New mean for NS: 0.000000
New range for EW: [-0.470, 0.530]
New mean for EW: -0.000000
New range for Z: [-0.441, 0.559]
New mean for Z: -0.000000

DNS = Detrended, Normalized, Shifted

North-South Stats:
DescribeResult(nobs=1228800, minmax=(-0.5152478241325915, 0.4847521758674085), mean=3.787609693476727e-16, variance=0.00022901459140630632, skewness=-0.1033085189717326, kurtosis=56.53872475095817)
median: 0.00012950548219936575
mode: ModeResult(mode=-0.5152478241325915, count=1)
standard deviation: 0.015133228056376447

East-West Stats:
DescribeResult(nobs=1228800, minmax=(-0.47034474769683, 0.5296552523031702), mean=-2.580379486472051e-16, variance=8.207605858568015e-05, skewness=-0.008233381277794327, kurtosis=149.3518793822338)
median: 3.5697448634880447e-05
mode: ModeResult(mode=-0.47034474769683, count=1)
standard deviation: 0.009059583797596946

Z-component Stats:
DescribeResult(nobs=1228800, minmax=(-0.441206505335003, 0.5587934946649971), mean=-1.9058684029108855e-16, variance=0.0005235396207434097, skewness=-0.09086115987043719, kurtosis=10.580487012146193)
median: 0.0002861539687265824
mode: ModeResult(mode=-0.441206505335003, count=1)
standard deviation: 0.022880988194206968
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
dataframe: df2
NS Min-Max normalized range: [0.000, 1.000]
EW Min-Max normalized range: [0.000, 1.000]
Z Min-Max normalized range: [0.000, 1.000]
New range for NS: [-0.502, 0.498]
New mean for NS: 0.000000
New range for EW: [-0.505, 0.495]
New mean for EW: -0.000000
New range for Z: [-0.512, 0.488]
New mean for Z: -0.000000

DNS = Detrended, Normalized, Shifted

North-South Stats:
DescribeResult(nobs=1228800, minmax=(-0.5019381220031599, 0.4980618779968399), mean=4.342417629181009e-16, variance=9.281385498144517e-05, skewness=-0.6297223640905917, kurtosis=493.89079662278203)
median: 2.1199030841523303e-05
mode: ModeResult(mode=-0.5152478241325915, count=1)
standard deviation: 0.009633994757183862

East-West Stats:
DescribeResult(nobs=1228800, minmax=(-0.5054436924811294, 0.4945563075188706), mean=-6.511935088382437e-17, variance=0.00012834331184863885, skewness=-0.08707246741895831, kurtosis=493.4782543586662)
median: -1.531246912561679e-05
mode: ModeResult(mode=-0.5054436924811294, count=1)
standard deviation: 0.01132887072256705

Z-component Stats:
DescribeResult(nobs=1228800, minmax=(-0.511524912555161, 0.48847508744483903), mean=-4.7809701799369124e-18, variance=0.00016620456012125071, skewness=-0.3346075729511631, kurtosis=67.8651994844411)
median: 5.935640950982535e-05
mode: ModeResult(mode=-0.511524912555161, count=1)
standard deviation: 0.012892034754888433
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
dataframe: df3
NS Min-Max normalized range: [0.000, 1.000]
EW Min-Max normalized range: [0.000, 1.000]
Z Min-Max normalized range: [0.000, 1.000]
New range for NS: [-0.500, 0.500]
New mean for NS: 0.000000
New range for EW: [-0.505, 0.495]
New mean for EW: 0.000000
New range for Z: [-0.580, 0.420]
New mean for Z: -0.000000

DNS = Detrended, Normalized, Shifted

North-South Stats:
DescribeResult(nobs=1228800, minmax=(-0.49994208758987224, 0.5000579124101278), mean=9.17677753809835e-17, variance=2.945972925212792e-05, skewness=0.6501268003686306, kurtosis=871.1111995058142)
median: -1.1423977730184998e-06
mode: ModeResult(mode=-0.5152478241325915, count=1)
standard deviation: 0.005427681756710559

East-West Stats:
DescribeResult(nobs=1228800, minmax=(-0.5045962431992747, 0.49540375680072524), mean=1.6304571083015917e-16, variance=6.386936893778217e-05, skewness=0.2222447495114245, kurtosis=526.0035362484331)
median: -4.021702497969404e-06
mode: ModeResult(mode=-0.5045962431992747, count=1)
standard deviation: 0.007991831388222657

Z-component Stats:
DescribeResult(nobs=1228800, minmax=(-0.5795712973134393, 0.42042870268656074), mean=-4.196021423837533e-16, variance=1.9544125053985618e-05, skewness=-2.4679640755390464, kurtosis=1886.793203472342)
median: -2.0765811693523872e-06
mode: ModeResult(mode=-0.5795712973134393, count=1)
standard deviation: 0.0044208737885157055
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
dataframe: df4
NS Min-Max normalized range: [0.000, 1.000]
EW Min-Max normalized range: [0.000, 1.000]
Z Min-Max normalized range: [0.000, 1.000]
New range for NS: [-0.504, 0.496]
New mean for NS: -0.000000
New range for EW: [-0.484, 0.516]
New mean for EW: 0.000000
New range for Z: [-0.522, 0.478]
New mean for Z: 0.000000

DNS = Detrended, Normalized, Shifted

North-South Stats:
DescribeResult(nobs=1228800, minmax=(-0.5035512895100599, 0.4964487104899403), mean=-1.6698448179752746e-16, variance=0.0003347398421525503, skewness=0.12254345842413947, kurtosis=90.85882133355828)
median: -4.582177470369153e-05
mode: ModeResult(mode=-0.5152478241325915, count=1)
standard deviation: 0.018295896866580286

East-West Stats:
DescribeResult(nobs=1228800, minmax=(-0.48401281650907285, 0.5159871834909271), mean=3.8022247387618316e-17, variance=0.00010135938094986332, skewness=0.11743914004407581, kurtosis=174.8677707538525)
median: -2.0929566298039104e-05
mode: ModeResult(mode=-0.48401281650907285, count=1)
standard deviation: 0.010067739614723117

Z-component Stats:
DescribeResult(nobs=1228800, minmax=(-0.5220450589073411, 0.4779549410926589), mean=2.4287285145992616e-16, variance=0.0011552934365230184, skewness=0.11061175651743019, kurtosis=10.871788758457647)
median: -0.0002585766612292484
mode: ModeResult(mode=-0.5220450589073411, count=1)
standard deviation: 0.033989607772421285
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
dataframe: df5
NS Min-Max normalized range: [0.000, 1.000]
EW Min-Max normalized range: [0.000, 1.000]
Z Min-Max normalized range: [0.000, 1.000]
New range for NS: [-0.510, 0.490]
New mean for NS: 0.000000
New range for EW: [-0.493, 0.507]
New mean for EW: 0.000000
New range for Z: [-0.497, 0.503]
New mean for Z: -0.000000

DNS = Detrended, Normalized, Shifted

North-South Stats:
DescribeResult(nobs=1228800, minmax=(-0.5096600529220939, 0.49033994707790607), mean=2.9693767699308836e-16, variance=0.00010415379382992493, skewness=-0.023853380096099826, kurtosis=371.55586172494714)
median: -2.5429592468872997e-05
mode: ModeResult(mode=-0.5152478241325915, count=1)
standard deviation: 0.010205576604480657

East-West Stats:
DescribeResult(nobs=1228800, minmax=(-0.49287762251997863, 0.5071223774800213), mean=1.3202329854355987e-17, variance=0.00013912613597184646, skewness=0.052231500088967535, kurtosis=174.31062086637456)
median: -2.8702646493461437e-06
mode: ModeResult(mode=-0.49287762251997863, count=1)
standard deviation: 0.011795174266277164

Z-component Stats:
DescribeResult(nobs=1228800, minmax=(-0.4972659843471705, 0.5027340156528295), mean=-1.5751018111326288e-16, variance=0.00014779390976688687, skewness=-0.033495388745043334, kurtosis=131.81490838854597)
median: -1.860860267985376e-05
mode: ModeResult(mode=-0.4972659843471705, count=1)
standard deviation: 0.012157051853426025
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

---

Subsampling the Time Series

Notes:

• the original sampling rate for the data is 1024 Hz
• different step sizes were applied to the normalized, detrended and mean-shifted (DNS) data for subsampling
• adjust x-axis limits to focus in on certain times

"percent_check" Function for Choosing Subsampling Step Size:

Notes:

• this method uses interpolation to compare subsampled data to the full DNS data
• the absolute error between the full DNS data and the reconstructed subsampled data is calculated and divided by the full data range
• this result is then used determine if the error is within the selected threshold (i.e. 5%)

NS results 1 (df): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9457%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 19.2395%'}
EW results 1 (df): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9919%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 16.9826%'}
Z results 1 (df): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.0938%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 69.2043%'}

NS results 1 (df2): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9462%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 20.9703%'}
EW results 1 (df2): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9166%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 18.6714%'}
Z results 1 (df2): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.3123%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 47.4195%'}

NS results 1 (df3): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9146%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 39.4024%'}
EW results 1 (df3): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.8758%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 36.5209%'}
Z results 1 (df3): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.8949%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 82.8238%'}

NS results 1 (df4): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.7948%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 16.6893%'}
EW results 1 (df4): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9743%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 19.5554%'}
Z results 1 (df4): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 95.9887%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 36.9399%'}

NS results 1 (df5): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.8687%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 29.3628%'}
EW results 1 (df5): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9373%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 18.6268%'}
Z results 1 (df5): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.5474%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 47.0429%'}

percent_check results:

• A step size of 7 was the largest that passed the percent_check test for NS, EW, and Z data simultaneously for all dataframes (plotted below)

dataframe: df

dataframe: df2

dataframe: df3

dataframe: df4

dataframe: df5

percent_check function using scipy.signal.decimate for y_subsampled instead of indexing:

• testing a different method for subsampling with the same step size (i.e. 7)

NS_results_test_1 (df): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9447%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 19.6512%'}
EW_results_test_1 (df): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9924%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 17.1854%'}
Z_results_test_1 (df): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 98.9932%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 56.3167%'}

NS_results_test_1 (df2): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9451%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 20.7711%'}
EW_results_test_1 (df2): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9145%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 18.5602%'}
Z_results_test_1 (df2): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 98.9080%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 40.9484%'}

NS_results_test_1 (df3): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.8774%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 39.9450%'}
EW_results_test_1 (df3): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.8002%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 40.7109%'}
Z_results_test_1 (df3): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.8956%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 56.4975%'}

NS_results_test_1 (df4): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.6542%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 18.0818%'}
EW_results_test_1 (df4): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9735%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 19.6565%'}
Z_results_test_1 (df4): {'step': 7, 'tolerance': '5.0%', 'passes': False, 'points_within_tolerance': ' 93.4352%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 39.5411%'}

NS_results_test_1 (df5): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.8494%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 30.5137%'}
EW_results_test_1 (df5): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9371%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 18.8787%'}
Z_results_test_1 (df5): {'step': 7, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.3926%', 'num_original_points': 1228800, 'num_subsampled_points': 175543, 'data_range': ' 1.0000', 'max_normalized_error': ' 42.2311%'}

Comparing percent_check results from scipy.signal.decimate and indexing for y_subsampled

• There were a similar percentage of points within the error tolerance when using the scipy.signal.decimate method compared to the indexing method for subsampling
• For later cells, the scipy.signal.decimate method will be used as it includes a built-in anti-aliasing filter

---

Tapering the Time Series

Notes:

• a Hann window/raised cosine was used to taper the DNS time series
• the data is tapered starting at 10% from the edges (this percentage can be adjusted)

dataframe: df

dataframe: df2

dataframe: df3

dataframe: df4

dataframe: df5

'percent_check_tapered' for tapered time series:

• a tapering version of the 'percent_check' function that was used for subsampling
• based on tapering starting at 10% from the data edges

NS_taper_results_1 (df): {'padding': 0, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9220%', 'max_normalized_error': ' 33.0174%', 'mean_abs_error': ' 0.0012', 'mae_as_%_of_std': ' 7.8978%', 'num_points': 1228800, 'data_range': ' 1.0000'}
EW_taper_results_1 (df): {'padding': 0, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9718%', 'max_normalized_error': ' 18.6478%', 'mean_abs_error': ' 0.0007', 'mae_as_%_of_std': ' 7.5137%', 'num_points': 1228800, 'data_range': ' 1.0000'}
Z_taper_results_1 (df): {'padding': 0, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.6984%', 'max_normalized_error': ' 17.8382%', 'mean_abs_error': ' 0.0021', 'mae_as_%_of_std': ' 9.2318%', 'num_points': 1228800, 'data_range': ' 1.0000'}

NS_taper_results_1 (df2): {'padding': 0, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.7722%', 'max_normalized_error': ' 42.0812%', 'mean_abs_error': ' 0.0008', 'mae_as_%_of_std': ' 7.9139%', 'num_points': 1228800, 'data_range': ' 1.0000'}
EW_taper_results_1 (df2): {'padding': 0, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.6724%', 'max_normalized_error': ' 42.4065%', 'mean_abs_error': ' 0.0009', 'mae_as_%_of_std': ' 8.0063%', 'num_points': 1228800, 'data_range': ' 1.0000'}
Z_taper_results_1 (df2): {'padding': 0, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9150%', 'max_normalized_error': ' 43.0695%', 'mean_abs_error': ' 0.0006', 'mae_as_%_of_std': ' 4.5780%', 'num_points': 1228800, 'data_range': ' 1.0000'}

NS_taper_results_1 (df3): {'padding': 0, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 100.0000%', 'max_normalized_error': ' 0.2580%', 'mean_abs_error': ' 0.0000', 'mae_as_%_of_std': ' 0.5296%', 'num_points': 1228800, 'data_range': ' 1.0000'}
EW_taper_results_1 (df3): {'padding': 0, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 100.0000%', 'max_normalized_error': ' 0.7747%', 'mean_abs_error': ' 0.0001', 'mae_as_%_of_std': ' 0.7245%', 'num_points': 1228800, 'data_range': ' 1.0000'}
Z_taper_results_1 (df3): {'padding': 0, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 100.0000%', 'max_normalized_error': ' 0.3323%', 'mean_abs_error': ' 0.0000', 'mae_as_%_of_std': ' 0.9960%', 'num_points': 1228800, 'data_range': ' 1.0000'}

NS_taper_results_1 (df4): {'padding': 0, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9749%', 'max_normalized_error': ' 11.3581%', 'mean_abs_error': ' 0.0010', 'mae_as_%_of_std': ' 5.4971%', 'num_points': 1228800, 'data_range': ' 1.0000'}
EW_taper_results_1 (df4): {'padding': 0, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9979%', 'max_normalized_error': ' 7.1650%', 'mean_abs_error': ' 0.0006', 'mae_as_%_of_std': ' 6.2506%', 'num_points': 1228800, 'data_range': ' 1.0000'}
Z_taper_results_1 (df4): {'padding': 0, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9240%', 'max_normalized_error': ' 26.9833%', 'mean_abs_error': ' 0.0015', 'mae_as_%_of_std': ' 4.5339%', 'num_points': 1228800, 'data_range': ' 1.0000'}

NS_taper_results_1 (df5): {'padding': 0, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9995%', 'max_normalized_error': ' 5.3728%', 'mean_abs_error': ' 0.0002', 'mae_as_%_of_std': ' 2.2915%', 'num_points': 1228800, 'data_range': ' 1.0000'}
EW_taper_results_1 (df5): {'padding': 0, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 100.0000%', 'max_normalized_error': ' 4.6122%', 'mean_abs_error': ' 0.0003', 'mae_as_%_of_std': ' 2.2257%', 'num_points': 1228800, 'data_range': ' 1.0000'}
Z_taper_results_1 (df5): {'padding': 0, 'tolerance': '5.0%', 'passes': True, 'points_within_tolerance': ' 99.9945%', 'max_normalized_error': ' 10.3885%', 'mean_abs_error': ' 0.0004', 'mae_as_%_of_std': ' 3.2572%', 'num_points': 1228800, 'data_range': ' 1.0000'}

---

Combining Subsampling and Tapering

Notes:

• The full series was tapered before subsampling
• A Hann window was used for tapering
• A step size of 7 was used for subsampling, consistent across the North-South, East-West, and Up-Down (Z) data
  • adjust the step size used for subsampling as needed

dataframe: df

dataframe: df2

dataframe: df3

dataframe: df4

dataframe: df5

---

Fast Fourier Transform

Notes:

• Applying the fast fourier transform to subsampled and tapered DNS data and plotting the resulting magnitude and phase spectra
  • (commented out phase spectra for now)
  • also defined a coherent gain function in attempt to correct for the amplitude reduction from windowing
    

Effects of subsampling/tapering: - removes higher frequency content - reduces spectral leakage caused by discontinuities

Coherent gain equation:

$G_c = \frac{1}{N}\sum_{n=0}^{N-1}\omega[n]$

• $G_c$: coherent gain
• $\omega[n]$: window
• $N$: window length

Approach 1: Overlay FFT results for tapered/subsampled data onto single figure with full DNS results

• plot for each dataframe as needed
  • may need to convert subsampled data from arrays to dataframes

dataframe: df

Horizontal and Vertical FFTs

• Goal: Add NS and EW FFTs together to get one set of plots (Horizontal)
• Leave Z FFT plots as is (Vertical), plotted from a previous cell

Horizontal FFT Plots:

horizontal FFT for dataframe: df

---

FFT With Moving Window

Notes:

• Goal: apply moving window (20 second intervals)
• Using short time fourier transform from scipy.signal
• Issue with previous version of code: time was not the same dimensions as the STFT result
  • Possible solutions: Plot spectrogram to show frequency content overtime, or plot average magnitude spectrum
• Tried log scale for spectrogram frequency axis, did not display well for most full data plots
• adjust y-axis limits to focus on areas of interest

Spectrograms

dataframe: df
Spectrograms for North-South data

Spectrograms for East-West data

Spectrograms for Z-component data

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
dataframe: df2
Spectrograms for North-South data

Spectrograms for East-West data

Spectrograms for Z-component data

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
dataframe: df3
Spectrograms for North-South data

Spectrograms for East-West data

Spectrograms for Z-component data

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
dataframe: df4
Spectrograms for North-South data

Spectrograms for East-West data

Spectrograms for Z-component data

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
dataframe: df5
Spectrograms for North-South data

Spectrograms for East-West data

Spectrograms for Z-component data

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

---

H/V Ratio

Notes:

• Divide horizontal magnitude by vertical magnitude to get H/V ratio
• Used vector-magnitude formula to combine horizontal magnitudes for North-South and East-West components

Filter for Smoothing

• applied Savitzky-Golay filter for smoothing data
  • also tried an envelope function for smoothing using the Hilbert transform
• limited displayed frequency range

dataframe: df
Full data peak frequency: 31.797500000000003 Hz
Full data peak H/V: 3.6743666357980906
Tapered/Subsampled data peak frequency: 30.686641693813723 Hz
Tapered/Subsampled data peak H/V: 3.937206179148854

Note: 30.63 +/- 3.81 Hz is the max. H/V from screenshot of Grilla average H/V plot

Interpreting Horizontal-to-Vertical Spectral Ratios

• Peaks should occur at fundamental and higher order resonance frequencies
  • (fundamental frequency = lowest resonant frequency in a system)
• Typically, the fundamental resonance frequency is the first/lowest value indicated by the highest amplitude peak on the H/V frequency spectrum
• H/V = 1 indicates that the horizontal and vertical motions are equal
• H/V < 1 indicates that horizontal motion is weaker than vertical motion
• H/V > 1 indicates that horizontal motion is stronger than vertical motion

Plotting H/V Ratio From Grilla .txt File:

Convert Cell Outputs to PDF:

• can currently download as .html file, which when opened in a browser can be saved as a pdf using print (Ctrl+P) -> save to pdf
  
  • using code to directly download as .pdf file is not working currently
  • if opened with Jupyter Notebook, can save full file as .pdf directly by going to File -> Save and Export Notebook As -> PDF

Created HTML file: Proj_2_File_1_Tyendinaga_Updated(1).html
Open this in your browser and use Ctrl+P --> Save as PDF
(The HTML file contains only outputs and markdown, no code cells)